We define oldforms and newforms for Drinfeld cusp forms of level t and conjecture that their direct sum is the whole space of cusp forms. Moreover we describe explicitly the matrix U associated to the action of the Atkin operator (Formula presented.) on cusp forms of level t and use it to compute tables of slopes of eigenforms. Building on such data, we formulate conjectures on bounds for slopes, on the diagonalizability of (Formula presented.) and on various other issues. Via the explicit form of the matrix U we are then able to verify our conjectures in various cases (mainly in small weights).

On the Structure and Slopes of Drinfeld Cusp Forms

Bandini A.;Valentino M.
2022-01-01

Abstract

We define oldforms and newforms for Drinfeld cusp forms of level t and conjecture that their direct sum is the whole space of cusp forms. Moreover we describe explicitly the matrix U associated to the action of the Atkin operator (Formula presented.) on cusp forms of level t and use it to compute tables of slopes of eigenforms. Building on such data, we formulate conjectures on bounds for slopes, on the diagonalizability of (Formula presented.) and on various other issues. Via the explicit form of the matrix U we are then able to verify our conjectures in various cases (mainly in small weights).
Atkin operator
Drinfeld cusp forms
Fricke involution
newforms and oldforms
slopes of eigenforms
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11770/341943
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 6
  • ???jsp.display-item.citation.isi??? ND
social impact